Anyonic interferometry is a powerful tool for processing topological quantum information. Anyonic interferometry may be used to non-demolitionally measure the collective anyonic charge of a group of (non-Abelian) anyons, without decohering internal state of the anyons, and consequently, anyonic interferometry may be used to generate braiding operators, change between different qubit encoding, and generate entangling gates.
By utilizing braiding operations and conventional, or complete, anyonic interferometry measurements for Ising-type quasiparticles, only the Clifford group operations, which is not computationally universal and, in fact, can be efficiently simulated on a classical/digital computer, can be generated.
Topological quantum computers based on Ising-type quasiparticles using only braiding operations and conventional/complete anyonic interferometry measurements lack a computationally universal set of topologically protected gates that may be applied to topological qubits.